Simplify the following expression: $\dfrac{12x}{8x^5}$ You can assume $x \neq 0$.
Explanation: $ \dfrac{12x}{8x^5} = \dfrac{12}{8} \cdot \dfrac{x}{x^5} $ To simplify $\frac{12}{8}$ , find the greatest common factor (GCD) of $12$ and $8$ $12 = 2 \cdot 2 \cdot 3$ $8 = 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(12, 8) = 2 \cdot 2 = 4 $ $ \dfrac{12}{8} \cdot \dfrac{x}{x^5} = \dfrac{4 \cdot 3}{4 \cdot 2} \cdot \dfrac{x}{x^5} $ $\phantom{ \dfrac{12}{8} \cdot \dfrac{1}{5}} = \dfrac{3}{2} \cdot \dfrac{x}{x^5} $ $ \dfrac{x}{x^5} = \dfrac{x}{x \cdot x \cdot x \cdot x \cdot x} = \dfrac{1}{x^4} $ $ \dfrac{3}{2} \cdot \dfrac{1}{x^4} = \dfrac{3}{2x^4} $